Prime Minister Jacinda Ardern has warned temporary visa holders who flout self-isolation rules that they will be liable for deportation.
Ardern said she had a message for those who had no consideration for the health of New Zealanders.
New Zealand would look after them but if they did not look after Kiwis, she warned: "frankly you are not welcome."
There were still only eight confirmed cases in New Zealand, but the global number jumped up by almost 11,000 overnight to 153,517, according to the World Health Organisation (WHO).
She told Newstalk ZB earlier on Monday she would be looking at forceful quarantine and potential deportation for people refusing to self-isolate for the required 14 days.
"If they do not self-isolate, I will have them quarantined and I'm looking at my deportation powers ... I take that very seriously."
Ardern said customs staff were now collecting the medical forms travellers were required to complete on arrival.
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The measures, which have been replicated in Australia, were some of the toughest border restrictions in the world amid the pandemic, but Ardern stood by the decision.
"Everything we've done thus far, people will see we're not afraid to take decisive action, we're not afraid to be world first.
"My primary focus here, of course ... [is] keeping New Zealanders safe."
She also told The AM Show the decisions made by the Government were based on expert advice. "We get the advice, we make the calls."
The restrictions would be reviewed in just over two weeks, but not lifted.
Cries of "we made it" could be heard from beaming arrivals at the international terminal.
"It is a point that we review our border controls, not necessarily lift them ... Everyone should prepare [for extensions]," she told The AM Show.
On Sunday, Auckland Airport was full of travellers trying to avoid the new rules, which took effect 1am on Monday morning.
Cries of "we made it" could be heard from beaming arrivals at the international terminal.
The new rules, which have been put in place to combat the spread of coronavirus, required every person entering New Zealand from anywhere in the world - excluding the Pacific - to distance themselves from others for 14 days.
Those in self-isolation should avoid social gatherings, work, school, child care facilities, university, religious gatherings, aged care and health facilities, prisons, sports gatherings, restaurants, and all public gatherings, according to the Ministry of Health website.
On Sunday, Prime Minister Jacinda Ardern told TVNZ's Q+A that self-isolation did not mean you would be quarantined to your apartment, hotel room or home for 14 days straight.
"You can take a walk around the block, but you can't go into public places and places where you're interacting with others," she told Q+A.
As part of enforcing that self-isolation, people entering NZ would have to fill in a form when they arrived at the border, Ardern said.
This would then be handed over to an airport nurse, who would then talk through the process and requirements of self-isolation.
Healthline would follow up with them. "Spot checks" for those required to self-isolate were on the table.
Non-compliant people could face quarantine measures, which would require them to enter a medical facility to be monitored.
Ardern said the facilities wouldn't act like a prison, but authorities could make sure there were people at the door "to make sure you don't leave".
Information regarding public gatherings was expected early this week, Ardern said.
The travel ban on China and Iran remained in place. Cruise ships were now banned from docking in New Zealand until at least June 30.
Ardern announced the new self-isolation rules on Saturday, saying they would slow down the spread of the virus.
"New Zealand has today, relative to other countries, a small number of cases," Ardern said during the announcement.
"We must plan and prepare for more cases. We must go hard and we must go early. We must do everything we can to protect the health of New Zealanders."
The country now had eight confirmed cases of coronavirus.
The original deadline for the measure was midnight Sunday.
Board of Airline Representatives NZ executive director Justin Tighe-Umbers said it had been pushed back an hour to reflect the reality of Sunday night flight patterns, when flights typically landed late in the evening.
The deadline referred to the time a plane touched down on the runway and passengers could come through border controls after 1am without needing to self-isolate, he said.
If you are unsure if you should be self-isolating, or if you do not know where you can go, contact Healthline for free on 0800 358 5453.